def plot_fig3c():
plot_mus = True # False #
edge = 'ac'
T, wis = 10, [5, 7, 9, 11, 13]
_, axs = get_axes(1, 1, .8)
deva = .6
data = np.empty(len(wis), dtype='object')
width_f = np.zeros(len(wis))
F = .006 # eV/angst
fmax = F * 1. / (3 * np.sqrt(3) * bond**2 / 4) * .4
a = .3
colors = ['red', 'blue', 'green', 'black', 'cyan', 'yellow']
for i, wi in enumerate(wis):
data[i] = get_stick_data('KC', T, '%s_stickTaito' % edge, wi)
width_f[i] = int_toAngst(wi, edge, key='width', C_C=bond)
print width_f
def axplusb(x, a, b):
return a * x + b
def Mmax(Lt, width_f, f):
def gfun(x):
return 0
def hfun(x):
return width_f / 2
def func(y, x):
return np.sqrt(x**2 + y**2)
return 2 * f * dblquad(func, 0, Lt, gfun, hfun)[0]
#thetas = width_f/(2*360/mus*1./(2*np.pi)*10)
def teor(theta, W0):
#return 2*np.sqrt(3)/9*1000*bond**3/W0*k*(1- 2*tau/(k*W0))**2*theta**3
return 2 * 2 * np.sqrt(3) / 9 * 1000 * bond**3 / W0 * k * (
1 - 2 * tau / (k * W0))**2 * theta**3
plot2 = []
plot3 = []
fit_vals = [
[.0007, .46],
[.0008, .4],
[.00075, .64],
[.00084, .705],
[.00085, .868],
]
fit_vals = [
[.00077, .6],
[.00077, .6],
[.00077, .6],
[.00077, .6],
[.00077, .6],
]
for j, wi in enumerate(wis):
LbLt = data[j]
LbLt.view('i8,i8').sort(order=['f0'], axis=0)
Rs = LbLt[:, 0] / (np.pi / 3.)
thetas = width_f[j] / (2 * Rs)
mus = thetas * 2. / width_f[j] * 360 / (2 * np.pi) * 10
print thetas
if wi == 5: m = 0
if wi == 7: m = 1
if wi == 9: m = 2
if wi == 11: m = 3
if wi == 13: m = 4
if plot_mus:
#plt.plot(mus, LbLt[:,1], '-o', color = colors[j],
# alpha = .8, label = r'width = %.2f\AA' %(width_f[j] + 2))
#a,b = curve_fit(axplusb, mus, LbLt[:,1]/LbLt[:,0], p0 = [1.,11])[0][:2]
#plt.plot(mus, LbLt[:,1]/LbLt[:,0], '-o', color = colors[j],
# alpha = .8, label = r'width = %.2f\AA' %(width_f[j] + 2))
#plt.plot(mus, a*mus + b, '--', color = colors[j],
# alpha = .8)
#plot2.append([width_f[j], -b/a])
#plt.plot(mus, LbLt[:,1]/width_f[j], '-o', color = colors[j],
# alpha = .8, label = r'width = %.2f\AA' %(width_f[j] + 2))
R_exp = width_f[j] / (2 * thetas)
add_L = np.sqrt(2 * R_exp * deva + deva**2) / 10.
axs[0].scatter(LbLt[:, 1] / 10 + add_L, mus, color=colors[m])
axs[0].text(3 + 1.5 / 4 * m,
11 - 7. / 4 * m,
r'w=%i' % wi,
color=colors[m])
else:
axs[0].plot(thetas, LbLt[:, 1], '-o', color=colors[m], alpha=.8)
'''
a,b = curve_fit(axplusb, thetas, LbLt[:,1]/LbLt[:,0], p0 = [1.,11])[0][:2]
plt.plot(thetas, LbLt[:,1]/LbLt[:,0], '-o', color = colors[j],
alpha = .8, label = r'width = %.2f\AA' %(width_f[j] + 2))
plt.plot(thetas, a*thetas + b, '--', color = colors[j],
alpha = .8)
plot2.append([width_f[j], -b/a])
'''
#plt.plot(thetas, LbLt[:,1]/LbLt[:,0], '-o', color = colors[j], alpha = .8)
print np.sqrt(width_f[j] / .01 * a + a**2)
def gfunc(Lt, theta, f, a):
L = np.sqrt(width_f[j] / theta * a + a**2) + Lt
return (1. / 6. * theta * k * width_f[j]**2 -
Mmax(L, width_f[j], f))**2
def Ltail(thetas, f, a):
Lts = np.zeros(len(thetas))
print f, a
for i, theta in enumerate(thetas):
Lts[i] = fmin(gfunc, 1, args=([theta, f, a]), disp=0)[0]
return Lts
def Ltail2(theta, f, a):
return fmin(gfunc, 1, args=([theta, f, a]), disp=0)[0]**2
Lmax = 55
Lts = np.linspace(0, Lmax, 15)
thts = np.linspace(0.005, .045, len(Lts))
teor_Lt = np.zeros(len(Lts))
if False:
fmax, a = curve_fit(Ltail, thetas, LbLt[:, 1], p0=[fmax, .2])[0]
else:
fmax, a = fit_vals[j]
print fmax, a
for i, Lt in enumerate(Lts):
#teor_theta[k] = 6*Mmax(Lt)/(k*width_f**2)
teor_Lt[i] = Ltail([thts[i]], fmax, a) + np.sqrt(
width_f[j] / thts[i] * deva +
deva**2) #fmin(gfunc, 1, args=([thts[i]]), disp = 0)[0]
#print thts[i], teor_Lt[i], 6*Mmax(teor_Lt[i], width_f[j])/(k*width_f[j]**2) - thts[i]
if plot_mus:
degs = thts * 2 / width_f[j] * 3600 / (2 * np.pi)
Lbend_teor = np.pi / 3 * width_f[j] / (2 * thts)
#plt.plot(degs, teor_Lt/Lbend_teor, '--', color = colors[j], label = 'width = %i' %wi)
#plt.plot(degs, teor_Lt/width_f[j], '--', color = colors[j], label = 'width = %i' %wi)
R_teor = width_f[j] / (2 * thts)
axs[0].plot(teor_Lt / 10,
degs,
'--',
color=colors[m],
label='width = %i' % wi)
theta0 = fmin(Ltail2, .001, args=([fmax, a]), disp=0)[0]
deg0 = theta0 * 2 / width_f[j] * 3600 / (2 * np.pi)
plot3.append([width_f[j], deg0, theta0])
else:
axs[0].plot(teor_Lt / 10,
thts,
'--',
color=colors[m],
label='width = %i' % wi)
#plt.legend(loc = 2, frameon = False)
if not plot_mus:
axs[0].set_ylabel(r'$\Theta$')
axs[0].set_xlabel(r'$L (nm)$')
else:
axs[0].set_ylabel(r'Curvature $\kappa$ (deg/nm)')
axs[0].set_xlabel(r'$L$ (nm)')
#axs[0].legend(loc = 2, frameon = False)
#axs[0].set_title('Required tail length for pinning')
axs[0].set_ylim([0, 13])
axs[0].set_xlim([1, 6])
axs[0].set_xticks(np.linspace(0, 7, 8))
a = plt.axes([.3, .675, .27, .23])
plot3 = np.array(plot3)
plt.plot(plot3[:, 0], plot3[:, 1], '--', color='black', alpha=.5)
for i in range(5):
plt.scatter(plot3[i, 0], plot3[i, 1], color=colors[i])
plt.yticks(np.linspace(.6, 2.2, 5))
plt.xticks(np.linspace(4, 16, 4))
plt.xlabel(r'Width (\AA)')
plt.ylabel(r'$\kappa$ (deg/nm)')
plt.show()
plot3 = np.array(plot3)
plt.plot(plot3[:, 0], plot3[:, 1], '-o')
plt.show()
plot3 = np.array(plot3)
plt.plot(plot3[:, 0], plot3[:, 2], '-o')
plt.show()
plot2 = np.array(plot2)
plt.plot(plot2[:, 0], plot2[:, 1], '-o')
plt.show()
def plot_fig3c():
plot_mus = True # False #
edge = 'ac'
T, wis = 10, [5, 7, 9, 11, 13]
_, axs = get_axes(1,1, .8)
deva = .6
data = np.empty(len(wis), dtype = 'object')
width_f = np.zeros(len(wis))
F = .006 # eV/angst
fmax = F*1./(3*np.sqrt(3)*bond**2/4)*.4
a = .3
colors = ['red', 'blue', 'green', 'black', 'cyan', 'yellow']
for i, wi in enumerate(wis):
data[i] = get_stick_data('KC', T, '%s_stickTaito' %edge, wi)
width_f[i] = int_toAngst(wi, edge, key='width', C_C = bond)
print width_f
def axplusb(x, a, b):
return a*x + b
def Mmax(Lt, width_f, f):
def gfun(x):
return 0
def hfun(x):
return width_f/2
def func(y,x):
return np.sqrt(x**2 + y**2)
return 2*f*dblquad(func, 0, Lt, gfun, hfun)[0]
#thetas = width_f/(2*360/mus*1./(2*np.pi)*10)
def teor(theta, W0):
#return 2*np.sqrt(3)/9*1000*bond**3/W0*k*(1- 2*tau/(k*W0))**2*theta**3
return 2*2*np.sqrt(3)/9*1000*bond**3/W0*k*(1- 2*tau/(k*W0))**2*theta**3
plot2 = []
plot3 = []
fit_vals = [[.0007, .46],
[.0008, .4],
[.00075, .64],
[.00084, .705],
[.00085, .868],]
fit_vals = [[.00077, .6],
[.00077, .6],
[.00077, .6],
[.00077, .6],
[.00077, .6],]
for j, wi in enumerate(wis):
LbLt = data[j]
LbLt.view('i8,i8').sort(order=['f0'], axis=0)
Rs = LbLt[:,0]/(np.pi/3.)
thetas = width_f[j]/(2*Rs)
mus = thetas*2./width_f[j]*360/(2*np.pi)*10
print thetas
if wi == 5: m = 0
if wi == 7: m = 1
if wi == 9: m = 2
if wi == 11: m = 3
if wi == 13: m = 4
if plot_mus:
#plt.plot(mus, LbLt[:,1], '-o', color = colors[j],
# alpha = .8, label = r'width = %.2f\AA' %(width_f[j] + 2))
#a,b = curve_fit(axplusb, mus, LbLt[:,1]/LbLt[:,0], p0 = [1.,11])[0][:2]
#plt.plot(mus, LbLt[:,1]/LbLt[:,0], '-o', color = colors[j],
# alpha = .8, label = r'width = %.2f\AA' %(width_f[j] + 2))
#plt.plot(mus, a*mus + b, '--', color = colors[j],
# alpha = .8)
#plot2.append([width_f[j], -b/a])
#plt.plot(mus, LbLt[:,1]/width_f[j], '-o', color = colors[j],
# alpha = .8, label = r'width = %.2f\AA' %(width_f[j] + 2))
R_exp = width_f[j]/(2*thetas)
add_L = np.sqrt(2*R_exp*deva + deva**2)/10.
axs[0].scatter(LbLt[:,1]/10 + add_L, mus, color = colors[m])
axs[0].text(3 + 1.5/4*m, 11 - 7./4*m, r'w=%i' %wi, color = colors[m])
else:
axs[0].plot(thetas, LbLt[:,1], '-o', color = colors[m], alpha = .8)
'''
a,b = curve_fit(axplusb, thetas, LbLt[:,1]/LbLt[:,0], p0 = [1.,11])[0][:2]
plt.plot(thetas, LbLt[:,1]/LbLt[:,0], '-o', color = colors[j],
alpha = .8, label = r'width = %.2f\AA' %(width_f[j] + 2))
plt.plot(thetas, a*thetas + b, '--', color = colors[j],
alpha = .8)
plot2.append([width_f[j], -b/a])
'''
#plt.plot(thetas, LbLt[:,1]/LbLt[:,0], '-o', color = colors[j], alpha = .8)
print np.sqrt(width_f[j]/.01*a + a**2)
def gfunc(Lt, theta, f, a):
L = np.sqrt(width_f[j]/theta*a + a**2) + Lt
return (1./6.*theta*k*width_f[j]**2 - Mmax(L, width_f[j], f))**2
def Ltail(thetas, f, a):
Lts = np.zeros(len(thetas))
print f, a
for i, theta in enumerate(thetas):
Lts[i] = fmin(gfunc, 1, args=([theta, f, a]), disp = 0)[0]
return Lts
def Ltail2(theta, f, a):
return fmin(gfunc, 1, args=([theta, f, a]), disp = 0)[0]**2
Lmax = 55
Lts = np.linspace(0, Lmax, 15)
thts = np.linspace(0.005, .045, len(Lts))
teor_Lt = np.zeros(len(Lts))
if False:
fmax, a = curve_fit(Ltail, thetas, LbLt[:,1], p0 = [fmax, .2])[0]
else:
fmax, a = fit_vals[j]
print fmax, a
for i, Lt in enumerate(Lts):
#teor_theta[k] = 6*Mmax(Lt)/(k*width_f**2)
teor_Lt[i] = Ltail([thts[i]], fmax ,a) + np.sqrt(width_f[j]/thts[i]*deva + deva**2) #fmin(gfunc, 1, args=([thts[i]]), disp = 0)[0]
#print thts[i], teor_Lt[i], 6*Mmax(teor_Lt[i], width_f[j])/(k*width_f[j]**2) - thts[i]
if plot_mus:
degs = thts*2/width_f[j]*3600/(2*np.pi)
Lbend_teor = np.pi/3*width_f[j]/(2*thts)
#plt.plot(degs, teor_Lt/Lbend_teor, '--', color = colors[j], label = 'width = %i' %wi)
#plt.plot(degs, teor_Lt/width_f[j], '--', color = colors[j], label = 'width = %i' %wi)
R_teor = width_f[j]/(2*thts)
axs[0].plot(teor_Lt/10, degs, '--', color = colors[m], label = 'width = %i' %wi)
theta0 = fmin(Ltail2, .001, args=([fmax, a]), disp = 0)[0]
deg0 = theta0*2/width_f[j]*3600/(2*np.pi)
plot3.append([width_f[j], deg0, theta0])
else:
axs[0].plot(teor_Lt/10, thts, '--', color = colors[m], label = 'width = %i' %wi)
#plt.legend(loc = 2, frameon = False)
if not plot_mus:
axs[0].set_ylabel(r'$\Theta$')
axs[0].set_xlabel(r'$L (nm)$')
else:
axs[0].set_ylabel(r'Curvature $\kappa$ (deg/nm)')
axs[0].set_xlabel(r'$L$ (nm)')
#axs[0].legend(loc = 2, frameon = False)
#axs[0].set_title('Required tail length for pinning')
axs[0].set_ylim([0,13])
axs[0].set_xlim([1,6])
axs[0].set_xticks(np.linspace(0, 7, 8))
a = plt.axes([.3, .675, .27, .23])
plot3 = np.array(plot3)
plt.plot(plot3[:,0], plot3[:,1], '--', color = 'black', alpha = .5)
for i in range(5):
plt.scatter(plot3[i,0], plot3[i,1], color = colors[i])
plt.yticks(np.linspace(.6, 2.2, 5))
plt.xticks(np.linspace(4, 16, 4))
plt.xlabel(r'Width (\AA)')
plt.ylabel(r'$\kappa$ (deg/nm)')
plt.show()
plot3 = np.array(plot3)
plt.plot(plot3[:,0], plot3[:,1], '-o')
plt.show()
plot3 = np.array(plot3)
plt.plot(plot3[:,0], plot3[:,2], '-o')
plt.show()
plot2 = np.array(plot2)
plt.plot(plot2[:,0], plot2[:,1], '-o')
plt.show()
def plot_stick2(edge):
plot_mus = True # False #
#edge = 'ac'
T, wis = 10, [5, 7, 9, 11, 13]
data = np.empty(len(wis), dtype = 'object')
width_f = np.zeros(len(wis))
F = .006 # eV/angst
fmax = F*1./(3*np.sqrt(3)*bond**2/4)*.4
a = .3
colors = ['blue', 'red', 'black', 'green', 'yellow']
#print fmax
for i, wi in enumerate(wis):
data[i] = get_stick_data('KC', T, '%s_stickTaito' %edge, wi)
width_f[i] = int_toAngst(wi, edge, key='width', C_C = bond)
print width_f
def axplusb(x, a, b):
return a*x + b
def Mmax(Lt, width_f, f):
def gfun(x):
return 0
def hfun(x):
return width_f/2
def func(y,x):
return np.sqrt(x**2 + y**2)
return 2*f*dblquad(func, 0, Lt, gfun, hfun)[0]
#thetas = width_f/(2*360/mus*1./(2*np.pi)*10)
def teor(theta, W0):
#return 2*np.sqrt(3)/9*1000*bond**3/W0*k*(1- 2*tau/(k*W0))**2*theta**3
return 2*2*np.sqrt(3)/9*1000*bond**3/W0*k*(1- 2*tau/(k*W0))**2*theta**3
plot2 = []
plot3 = []
fit_vals = [[.0007, .46],
[.0008, .4],
[.00075, .64],
[.00084, .705],
[.00085, .868],]
fit_vals = [[.00077, .6],
[.00077, .6],
[.00077, .6],
[.00077, .6],
[.00077, .6],]
for j, wi in enumerate(wis):
LbLt = data[j]
LbLt.view('i8,i8').sort(order=['f0'], axis=0)
Rs = LbLt[:,0]/(np.pi/3.)
thetas = width_f[j]/(2*Rs)
mus = thetas*2./width_f[j]*360/(2*np.pi)*10
print thetas
'''
if plot_mus:
for i in range(len(mus)):
if LbLt[i,1] < 3:
print 'hoos'
plt.scatter(mus[i], LbLt[i,1]/LbLt[i,0], marker = 'D',color = 'red')
else:
plt.scatter(mus[i], LbLt[i,1]/LbLt[i,0], color = 'blue')
plt.scatter(mus, teor(thetas, width_f), marker = 'v', label = 'teor')
plt.plot([2,2], [0, .4], '--', color = 'black')
plt.plot([4,4], [0, .4], '--', color = 'black')
plt.text(1.03, .4, 'experimetl stick below 2deg/angst')
plt.text(1.03, -.05, 'red squares only one unit cell \n enought to hold bend')
plt.text(3.7, .4, 'buckling')
plt.title('Reguired tail length for bend to stick ac, w=7')
plt.legend(loc = 2, frameon = False)
plt.xlabel('Deg/angst')
plt.ylabel('Ltail/Lbend')
plt.show()
else:
'''
if plot_mus:
#plt.plot(mus, LbLt[:,1], '-o', color = colors[j],
# alpha = .8, label = r'width = %.2f\AA' %(width_f[j] + 2))
#a,b = curve_fit(axplusb, mus, LbLt[:,1]/LbLt[:,0], p0 = [1.,11])[0][:2]
#plt.plot(mus, LbLt[:,1]/LbLt[:,0], '-o', color = colors[j],
# alpha = .8, label = r'width = %.2f\AA' %(width_f[j] + 2))
#plt.plot(mus, a*mus + b, '--', color = colors[j],
# alpha = .8)
#plot2.append([width_f[j], -b/a])
#plt.plot(mus, LbLt[:,1]/width_f[j], '-o', color = colors[j],
# alpha = .8, label = r'width = %.2f\AA' %(width_f[j] + 2))
R_exp = width_f[j]/(2*thetas)
plt.plot(mus, LbLt[:,1]/R_exp, '-o', color = colors[j],
alpha = .8, label = r'width = %.2f\AA' %(width_f[j] + 2))
else:
plt.plot(thetas, LbLt[:,1], '-o', color = colors[j], alpha = .8)
'''
a,b = curve_fit(axplusb, thetas, LbLt[:,1]/LbLt[:,0], p0 = [1.,11])[0][:2]
plt.plot(thetas, LbLt[:,1]/LbLt[:,0], '-o', color = colors[j],
alpha = .8, label = r'width = %.2f\AA' %(width_f[j] + 2))
plt.plot(thetas, a*thetas + b, '--', color = colors[j],
alpha = .8)
plot2.append([width_f[j], -b/a])
'''
#plt.plot(thetas, LbLt[:,1]/LbLt[:,0], '-o', color = colors[j], alpha = .8)
print np.sqrt(width_f[j]/.01*a + a**2)
def gfunc(Lt, theta, f, a):
L = np.sqrt(width_f[j]/theta*a + a**2) + Lt
return (1./6.*theta*k*width_f[j]**2 - Mmax(L, width_f[j], f))**2
def Ltail(thetas, f, a):
Lts = np.zeros(len(thetas))
print f, a
for i, theta in enumerate(thetas):
Lts[i] = fmin(gfunc, 1, args=([theta, f, a]), disp = 0)[0]
return Lts
def Ltail2(theta, f, a):
return fmin(gfunc, 1, args=([theta, f, a]), disp = 0)[0]**2
Lmax = 35
Lts = np.linspace(0, Lmax, 15)
thts = np.linspace(0.005, .04, len(Lts))
teor_Lt = np.zeros(len(Lts))
if False:
fmax, a = curve_fit(Ltail, thetas, LbLt[:,1], p0 = [fmax, .2])[0]
else:
fmax, a = fit_vals[j]
print fmax, a
for i, Lt in enumerate(Lts):
#teor_theta[k] = 6*Mmax(Lt)/(k*width_f**2)
teor_Lt[i] = Ltail([thts[i]], fmax ,a) #fmin(gfunc, 1, args=([thts[i]]), disp = 0)[0]
#print thts[i], teor_Lt[i], 6*Mmax(teor_Lt[i], width_f[j])/(k*width_f[j]**2) - thts[i]
if plot_mus:
degs = thts*2/width_f[j]*3600/(2*np.pi)
Lbend_teor = np.pi/3*width_f[j]/(2*thts)
#plt.plot(degs, teor_Lt/Lbend_teor, '--', color = colors[j], label = 'width = %i' %wi)
#plt.plot(degs, teor_Lt/width_f[j], '--', color = colors[j], label = 'width = %i' %wi)
R_teor = width_f[j]/(2*thts)
plt.plot(degs, teor_Lt/R_teor, '--', color = colors[j], label = 'width = %i' %wi)
theta0 = fmin(Ltail2, .001, args=([fmax, a]), disp = 0)[0]
deg0 = theta0*2/width_f[j]*3600/(2*np.pi)
plot3.append([width_f[j], deg0, theta0])
else:
plt.plot(thts, teor_Lt, '--', color = colors[j], label = 'width = %i' %wi)
#plt.legend(loc = 2, frameon = False)
if not plot_mus:
plt.xlabel('Theta')
plt.ylabel('Ltail Angst')
else:
plt.xlabel('Curve deg/Angst')
plt.ylabel('Ltail Angst')
plt.legend(loc = 2, frameon = False)
plt.title('Required tail length for pinning')
plt.show()
plot3 = np.array(plot3)
plt.plot(plot3[:,0], plot3[:,1], '-o')
plt.show()
plot3 = np.array(plot3)
plt.plot(plot3[:,0], plot3[:,2], '-o')
plt.show()
plot2 = np.array(plot2)
plt.plot(plot2[:,0], plot2[:,1], '-o')
plt.show()
def plot_stick():
#width_f = 7.5
#print 4./360*2*np.pi*width_f/10/2.
#exit()
plot_mus = False
edge = 'ac'
T, wi = 10, 11
LbLt = get_stick_data('KC', T, '%s_stickTaito' %edge, wi)
LbLt.view('i8,i8').sort(order=['f0'], axis=0)
width_f = int_toAngst(wi, edge, key='width', C_C = bond)
Rs = LbLt[:,0]/(np.pi/3.)
thetas = width_f/(2*Rs)
mus = thetas*2./width_f*360/(2*np.pi)*10
#thetas = width_f/(2*360/mus*1./(2*np.pi)*10)
def teor(theta, W0):
#return 2*np.sqrt(3)/9*1000*bond**3/W0*k*(1- 2*tau/(k*W0))**2*theta**3
return 2*2*np.sqrt(3)/9*1000*bond**3/W0*k*(1- 2*tau/(k*W0))**2*theta**3
if plot_mus:
for i in range(len(mus)):
if LbLt[i,1] < 3:
print 'hoos'
plt.scatter(mus[i], LbLt[i,1]/LbLt[i,0], marker = 'D',color = 'red')
else:
plt.scatter(mus[i], LbLt[i,1]/LbLt[i,0], color = 'blue')
plt.scatter(mus, teor(thetas, width_f), marker = 'v', label = 'teor')
plt.plot([2,2], [0, .4], '--', color = 'black')
plt.plot([4,4], [0, .4], '--', color = 'black')
plt.text(1.03, .4, 'experimetl stick below 2deg/angst')
plt.text(1.03, -.05, 'red squares only one unit cell \n enought to hold bend')
plt.text(3.7, .4, 'buckling')
plt.title('Reguired tail length for bend to stick ac, w=7')
plt.legend(loc = 2, frameon = False)
plt.xlabel('Deg/angst')
plt.ylabel('Ltail/Lbend')
plt.show()
else:
for i in range(len(mus)):
if LbLt[i,1] < 3:
print 'hoos'
plt.scatter(thetas[i], LbLt[i,1]/LbLt[i,0], marker = 'D',color = 'red')
#plt.scatter(thetas[i], LbLt[i,1], marker = 'D',color = 'red')
else:
plt.scatter(thetas[i], LbLt[i,1]/LbLt[i,0], color = 'blue')
#plt.scatter(thetas[i], LbLt[i,1], color = 'blue')
print LbLt[i,1]/(np.pi/3)*2*thetas[i]/width_f, LbLt[i,1], 1/(np.pi/3)*2*thetas[i]/width_f, LbLt[i,0]
#plt.scatter(thetas, teor(thetas, width_f), marker = 'v', label = 'teor')
#plt.scatter(thetas, teor(thetas, width_f)*LbLt[:,0], marker = 'v', label = 'teor')
plt.twinx()
plt.scatter(thetas, LbLt[:,0])
plt.scatter(thetas, LbLt[:,1])
plt.legend(loc = 2, frameon = False)
plt.xlabel('Theta')
plt.ylabel('Ltail Angst')
plt.show()
def plot_stick2(edge):
plot_mus = True # False #
#edge = 'ac'
T, wis = 10, [5, 7, 9, 11, 13]
data = np.empty(len(wis), dtype='object')
width_f = np.zeros(len(wis))
F = .006 # eV/angst
fmax = F * 1. / (3 * np.sqrt(3) * bond**2 / 4) * .4
a = .3
colors = ['blue', 'red', 'black', 'green', 'yellow']
#print fmax
for i, wi in enumerate(wis):
data[i] = get_stick_data('KC', T, '%s_stickTaito' % edge, wi)
width_f[i] = int_toAngst(wi, edge, key='width', C_C=bond)
print width_f
def axplusb(x, a, b):
return a * x + b
def Mmax(Lt, width_f, f):
def gfun(x):
return 0
def hfun(x):
return width_f / 2
def func(y, x):
return np.sqrt(x**2 + y**2)
return 2 * f * dblquad(func, 0, Lt, gfun, hfun)[0]
#thetas = width_f/(2*360/mus*1./(2*np.pi)*10)
def teor(theta, W0):
#return 2*np.sqrt(3)/9*1000*bond**3/W0*k*(1- 2*tau/(k*W0))**2*theta**3
return 2 * 2 * np.sqrt(3) / 9 * 1000 * bond**3 / W0 * k * (
1 - 2 * tau / (k * W0))**2 * theta**3
plot2 = []
plot3 = []
fit_vals = [
[.0007, .46],
[.0008, .4],
[.00075, .64],
[.00084, .705],
[.00085, .868],
]
fit_vals = [
[.00077, .6],
[.00077, .6],
[.00077, .6],
[.00077, .6],
[.00077, .6],
]
for j, wi in enumerate(wis):
LbLt = data[j]
LbLt.view('i8,i8').sort(order=['f0'], axis=0)
Rs = LbLt[:, 0] / (np.pi / 3.)
thetas = width_f[j] / (2 * Rs)
mus = thetas * 2. / width_f[j] * 360 / (2 * np.pi) * 10
print thetas
'''
if plot_mus:
for i in range(len(mus)):
if LbLt[i,1] < 3:
print 'hoos'
plt.scatter(mus[i], LbLt[i,1]/LbLt[i,0], marker = 'D',color = 'red')
else:
plt.scatter(mus[i], LbLt[i,1]/LbLt[i,0], color = 'blue')
plt.scatter(mus, teor(thetas, width_f), marker = 'v', label = 'teor')
plt.plot([2,2], [0, .4], '--', color = 'black')
plt.plot([4,4], [0, .4], '--', color = 'black')
plt.text(1.03, .4, 'experimetl stick below 2deg/angst')
plt.text(1.03, -.05, 'red squares only one unit cell \n enought to hold bend')
plt.text(3.7, .4, 'buckling')
plt.title('Reguired tail length for bend to stick ac, w=7')
plt.legend(loc = 2, frameon = False)
plt.xlabel('Deg/angst')
plt.ylabel('Ltail/Lbend')
plt.show()
else:
'''
if plot_mus:
#plt.plot(mus, LbLt[:,1], '-o', color = colors[j],
# alpha = .8, label = r'width = %.2f\AA' %(width_f[j] + 2))
#a,b = curve_fit(axplusb, mus, LbLt[:,1]/LbLt[:,0], p0 = [1.,11])[0][:2]
#plt.plot(mus, LbLt[:,1]/LbLt[:,0], '-o', color = colors[j],
# alpha = .8, label = r'width = %.2f\AA' %(width_f[j] + 2))
#plt.plot(mus, a*mus + b, '--', color = colors[j],
# alpha = .8)
#plot2.append([width_f[j], -b/a])
#plt.plot(mus, LbLt[:,1]/width_f[j], '-o', color = colors[j],
# alpha = .8, label = r'width = %.2f\AA' %(width_f[j] + 2))
R_exp = width_f[j] / (2 * thetas)
plt.plot(mus,
LbLt[:, 1] / R_exp,
'-o',
color=colors[j],
alpha=.8,
label=r'width = %.2f\AA' % (width_f[j] + 2))
else:
plt.plot(thetas, LbLt[:, 1], '-o', color=colors[j], alpha=.8)
'''
a,b = curve_fit(axplusb, thetas, LbLt[:,1]/LbLt[:,0], p0 = [1.,11])[0][:2]
plt.plot(thetas, LbLt[:,1]/LbLt[:,0], '-o', color = colors[j],
alpha = .8, label = r'width = %.2f\AA' %(width_f[j] + 2))
plt.plot(thetas, a*thetas + b, '--', color = colors[j],
alpha = .8)
plot2.append([width_f[j], -b/a])
'''
#plt.plot(thetas, LbLt[:,1]/LbLt[:,0], '-o', color = colors[j], alpha = .8)
print np.sqrt(width_f[j] / .01 * a + a**2)
def gfunc(Lt, theta, f, a):
L = np.sqrt(width_f[j] / theta * a + a**2) + Lt
return (1. / 6. * theta * k * width_f[j]**2 -
Mmax(L, width_f[j], f))**2
def Ltail(thetas, f, a):
Lts = np.zeros(len(thetas))
print f, a
for i, theta in enumerate(thetas):
Lts[i] = fmin(gfunc, 1, args=([theta, f, a]), disp=0)[0]
return Lts
def Ltail2(theta, f, a):
return fmin(gfunc, 1, args=([theta, f, a]), disp=0)[0]**2
Lmax = 35
Lts = np.linspace(0, Lmax, 15)
thts = np.linspace(0.005, .04, len(Lts))
teor_Lt = np.zeros(len(Lts))
if False:
fmax, a = curve_fit(Ltail, thetas, LbLt[:, 1], p0=[fmax, .2])[0]
else:
fmax, a = fit_vals[j]
print fmax, a
for i, Lt in enumerate(Lts):
#teor_theta[k] = 6*Mmax(Lt)/(k*width_f**2)
teor_Lt[i] = Ltail(
[thts[i]], fmax,
a) #fmin(gfunc, 1, args=([thts[i]]), disp = 0)[0]
#print thts[i], teor_Lt[i], 6*Mmax(teor_Lt[i], width_f[j])/(k*width_f[j]**2) - thts[i]
if plot_mus:
degs = thts * 2 / width_f[j] * 3600 / (2 * np.pi)
Lbend_teor = np.pi / 3 * width_f[j] / (2 * thts)
#plt.plot(degs, teor_Lt/Lbend_teor, '--', color = colors[j], label = 'width = %i' %wi)
#plt.plot(degs, teor_Lt/width_f[j], '--', color = colors[j], label = 'width = %i' %wi)
R_teor = width_f[j] / (2 * thts)
plt.plot(degs,
teor_Lt / R_teor,
'--',
color=colors[j],
label='width = %i' % wi)
theta0 = fmin(Ltail2, .001, args=([fmax, a]), disp=0)[0]
deg0 = theta0 * 2 / width_f[j] * 3600 / (2 * np.pi)
plot3.append([width_f[j], deg0, theta0])
else:
plt.plot(thts,
teor_Lt,
'--',
color=colors[j],
label='width = %i' % wi)
#plt.legend(loc = 2, frameon = False)
if not plot_mus:
plt.xlabel('Theta')
plt.ylabel('Ltail Angst')
else:
plt.xlabel('Curve deg/Angst')
plt.ylabel('Ltail Angst')
plt.legend(loc=2, frameon=False)
plt.title('Required tail length for pinning')
plt.show()
plot3 = np.array(plot3)
plt.plot(plot3[:, 0], plot3[:, 1], '-o')
plt.show()
plot3 = np.array(plot3)
plt.plot(plot3[:, 0], plot3[:, 2], '-o')
plt.show()
plot2 = np.array(plot2)
plt.plot(plot2[:, 0], plot2[:, 1], '-o')
plt.show()
def plot_stick():
#width_f = 7.5
#print 4./360*2*np.pi*width_f/10/2.
#exit()
plot_mus = False
edge = 'ac'
T, wi = 10, 11
LbLt = get_stick_data('KC', T, '%s_stickTaito' % edge, wi)
LbLt.view('i8,i8').sort(order=['f0'], axis=0)
width_f = int_toAngst(wi, edge, key='width', C_C=bond)
Rs = LbLt[:, 0] / (np.pi / 3.)
thetas = width_f / (2 * Rs)
mus = thetas * 2. / width_f * 360 / (2 * np.pi) * 10
#thetas = width_f/(2*360/mus*1./(2*np.pi)*10)
def teor(theta, W0):
#return 2*np.sqrt(3)/9*1000*bond**3/W0*k*(1- 2*tau/(k*W0))**2*theta**3
return 2 * 2 * np.sqrt(3) / 9 * 1000 * bond**3 / W0 * k * (
1 - 2 * tau / (k * W0))**2 * theta**3
if plot_mus:
for i in range(len(mus)):
if LbLt[i, 1] < 3:
print 'hoos'
plt.scatter(mus[i],
LbLt[i, 1] / LbLt[i, 0],
marker='D',
color='red')
else:
plt.scatter(mus[i], LbLt[i, 1] / LbLt[i, 0], color='blue')
plt.scatter(mus, teor(thetas, width_f), marker='v', label='teor')
plt.plot([2, 2], [0, .4], '--', color='black')
plt.plot([4, 4], [0, .4], '--', color='black')
plt.text(1.03, .4, 'experimetl stick below 2deg/angst')
plt.text(1.03, -.05,
'red squares only one unit cell \n enought to hold bend')
plt.text(3.7, .4, 'buckling')
plt.title('Reguired tail length for bend to stick ac, w=7')
plt.legend(loc=2, frameon=False)
plt.xlabel('Deg/angst')
plt.ylabel('Ltail/Lbend')
plt.show()
else:
for i in range(len(mus)):
if LbLt[i, 1] < 3:
print 'hoos'
plt.scatter(thetas[i],
LbLt[i, 1] / LbLt[i, 0],
marker='D',
color='red')
#plt.scatter(thetas[i], LbLt[i,1], marker = 'D',color = 'red')
else:
plt.scatter(thetas[i], LbLt[i, 1] / LbLt[i, 0], color='blue')
#plt.scatter(thetas[i], LbLt[i,1], color = 'blue')
print LbLt[i, 1] / (np.pi / 3) * 2 * thetas[i] / width_f, LbLt[
i, 1], 1 / (np.pi / 3) * 2 * thetas[i] / width_f, LbLt[i, 0]
#plt.scatter(thetas, teor(thetas, width_f), marker = 'v', label = 'teor')
#plt.scatter(thetas, teor(thetas, width_f)*LbLt[:,0], marker = 'v', label = 'teor')
plt.twinx()
plt.scatter(thetas, LbLt[:, 0])
plt.scatter(thetas, LbLt[:, 1])
plt.legend(loc=2, frameon=False)
plt.xlabel('Theta')
plt.ylabel('Ltail Angst')
plt.show()
